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The Quantum Alternating Operator Ansatz (QAOA) and its predecessor, the Quantum Approximate Optimization Algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems.
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There exist also more sophisticated convex combinations, where the coefficients in front of H I H_{I} and C C are non-linear functions of t t (see [ 19 ] ). Allowing for such problem-specific coefficients can improve the convergence rate of the QAA significantly
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Otherwise consider B ~ : = B − λ min 𝟙 \tilde{B}\mathrel{\mathop{:}}\mathrel{\mkern-1.2mu}=B-\lambda_{\min}\mathds{1} and C ~ = C − λ min 𝟙 \tilde{C}=C-\lambda_{\min}\mathds{1} , where λ min < 0 \lambda_{\min}<0 is the smallest eigenvalue of C C . Then H lin ( B ~ , C ~ ) = H lin ( B , C ) − λ min 𝟙 H_{\lin(\tilde{B},\tilde{C})}=H_{\lin(B,C)}-\lambda_{\min}\mathds{1} generates the same time evolution as H lin ( B , C ) H_{\lin(B,C)} up to a global phase
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2022
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